A secret sharing scheme is a cryptographic technique used to protect the confidentiality of a message by dividing it into a number of pieces called shares. A secret sharing scheme has two main parts: a message sharing algorithm for dividing the message into shares and a message reconstruction algorithm for recovering the message from all of or a subset of the shares. Secret sharing can be used to store sensitive information (e.g., confidential data), authentication credentials (e.g., passwords) or cryptographic materials (e.g., cryptographic keys) securely in distributed systems or similar systems. A secret sharing scheme involves three roles: a dealer, at least two share-holders, and the receiver. The dealer is the party that has a message and executes the message sharing algorithm. The dealer generates a plurality of shares that are responsive to a determined threshold. The threshold is the minimum number of shares needed to be received by the receiver in order to recover the original message out of the total outstanding shares (the maximum threshold). After operating the sharing algorithm on the message to obtain the shares, the dealer distributes the shares to the share-holders. The receiver is the party attempting to reconstruct the message. When the receiver wants to learn the message, it collects shares from an authorized set of share-holders and assembles the shares to pass through the message reconstruction algorithm. If enough shares are available to reconstruct the original message, then the receiver recovers the message by executing the message reconstruction algorithm. The receiver may collect additional shares past the threshold. Note that dealers and receivers are typically programmed hardware or software entities, and not humans, whereas share-holders are typically humans employing various media such as paper, smartcards, or USB sticks.